- Propositional logic: language, deduction system, semantics, soundness, completeness;
- First-order logic: syntax, semantics, soundness, completeness, compactness;
- Set theory: fundamental axioms, ordinals, cardinals, transfinite induction, axiom of choice, continuum hypothesis;
- Computability: computable functions, λ-calculi, simple theory of types;
- Constructive mathematics: intuitionistic logic, propositions as types, normalisation;
- Limiting results: Peano arithmetic, Gödel’s incompleteness theorems, natural incompleteness results.
The slides of the course are available: select the right academic year
Here are some exercises on natural deduction.
The non-official videos are now available in the video page.
Results (academic year 2019/20)